Let's Do Turbulence Right: In Space and Time!
Abstract
The three-dimensional Navier-Stokes equations govern fluid turbulence, a chaotic and non-linear physical phenomenon characterized by complex eddies interacting across vast spatial and temporal scales. A numerically accurate modeling of this multi-scale energy cascade requires fully resolving both the fine spatial structures and the continuous temporal evolution of the flow field. In this paper, we leverage massive, time-resolved direct numerical simulations, which exceed 28 TB per run, to assess how numerical choices govern the resolved (3+1)-dimensional physics of turbulent flows. Building on this analysis, we study how neural networks represent the recorded turbulent motion. Our results highlight that spatial and temporal assessments can disagree for both numerical records and learned representations. We therefore call on the machine learning community to treat (3+1)-dimensional turbulence as a four-dimensional phenomenon.
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BibTeX
@misc{plattner2026lets,
title = {{Let's Do Turbulence Right: In Space and Time!}},
author = {Maximilian Plattner and Fabian Paischer and Johannes Brandstetter},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32601},
eprint = {2610.32601},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32601},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Let's Do Turbulence Right: In Space and Time!
AU - Maximilian Plattner
AU - Fabian Paischer
AU - Johannes Brandstetter
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32601
UR - https://arxiv.org/abs/2610.32601
AB - The three-dimensional Navier-Stokes equations govern fluid turbulence, a chaotic and non-linear physical phenomenon characterized by complex eddies interacting across vast spatial and temporal scales. A numerically accurate modeling of this multi-scale energy cascade requires fully resolving both the fine spatial structures and the continuous temporal evolution of the flow field. In this paper, we leverage massive, time-resolved direct numerical simulations, which exceed 28 TB per run, to assess how numerical choices govern the resolved (3+1)-dimensional physics of turbulent flows. Building on this analysis, we study how neural networks represent the recorded turbulent motion. Our results highlight that spatial and temporal assessments can disagree for both numerical records and learned representations. We therefore call on the machine learning community to treat (3+1)-dimensional turbulence as a four-dimensional phenomenon.
ER -